Chaperone-Assisted Translocation of a Polymer through a Nanopore

Na+-Mg2+ ion effects on conformation and translocation dynamics of single-stranded RNA: Cooperation and competition

The nanopore-based translocation of a single-stranded RNA (ssRNA) in mixed salt solution has garnered increasing interest for its biological and technological significance. However, it is challenging to comprehensively understand the effects of the mixed ion species on the translocation dynamics due to their cooperation and competition, which can be directly reflected by the ion screening and neutralizing effects, respectively. In this study, Langevin dynamics simulation is employed to investigate the properties of ssRNA conformation and translocation in mixed Na+-Mg2+ ion environments. Simulation results reveal that the ion screening effect dominates the change in the ssRNA conformational size, the ion neutralizing effect controls the capture rate of the ssRNA by the nanopore, and both of them take charge of the different changes in translocation time of the ssRNA under various mixed ion environments. Under high Na+ ion concentration, as Mg2+ concentration increases, the ion neutralizing effect strengthens, weakening the driving force inside the nanopore, leading to longer translocation time. Conversely, at low Na+ concentration, an increase in Mg2+ concentration enhances the ion screening effect, aiding in faster translocation. Furthermore, these simulation results will be explained by quantitative analysis, advancing a deeper understanding of the complicated effects of the mixed Na+-Mg2+ ions.

Crowding induced switching of polymer translocation by the amalgamation of entropy and osmotic pressure

The translocation of polymers is omnipresent in inherently crowded biological systems. We investigate the dynamics of polymer translocation through a pore in free and crowded environments using Langevin dynamics simulation. We observed a location-dependent translocation rate of monomers showcasing counterintuitive behavior in stark contrast to the bead velocity along the polymer backbone. The free energy calculation of asymmetrically placed polymers indicates a critical number of segments to direct receiver-side translocation. For one-sided crowding, we have identified a critical crowding size revealing a nonzero probability of translocation toward the crowded-side. Moreover, we have observed that shifting the polymer toward the crowded-side compensates for one-sided crowding, yielding an equal probability akin to a crowder-free system. In two-sided crowding, a slight variation in crowder size and packing fraction induces a polymer to switch its translocation direction. These conspicuous yet counter-intuitive phenomena are rationalized by minimalistic theoretical arguments based on osmotic pressure and radial entropic forces.

Polymer translocation: Effects of confinement

We investigate the influence of varying confinement on the dynamics of polymer translocation through a cone-shaped channel. For this, a linear polymer chain is modeled using self-avoiding walks on a square lattice. The cis side of a cone-shaped channel has a finite volume, while the trans side has a semi-infinite space. The confining environment is varied either by changing the position of the back wall while keeping the apex angle fixed or altering the apex angle while keeping the position of the back wall fixed. In both cases, the effective space ϕ, which represents the number of monomers in a chain relative to the total number of accessible sites within the cone, is reduced due to the imposed confinement. Consequently, the translocation dynamics are affected. We analyze the entropy of the confined system as a function of ϕ, which exhibits nonmonotonic behavior. We also calculate the free energy associated with the confinement as a function of a virtual coordinate for different positions of the back wall (base of the cone) along the conical axis for various apex angles. Employing the Fokker-Planck equation, we calculate the translocation time as a function of ϕ for different solvent conditions across the channel. Our findings indicate that the translocation time decreases as ϕ increases, but it eventually reaches a saturation point at a certain value of ϕ. Moreover, we highlight the possibility of controlling the translocation dynamics by manipulating the solvent quality across the channel. Furthermore, our investigation delves into the intricacies of polymer translocation through a cone-shaped channel, considering both repulsive and neutral interactions with the channel wall. This exploration unveils nuanced dynamics and sheds light on the factors that significantly impact translocation within confined channels.

Polymer Translocation and Nanopore Sequencing: A Review of Advances and Challenges

Various biological processes involve the translocation of macromolecules across nanopores; these pores are basically protein channels embedded in membranes. Understanding the mechanism of translocation is crucial to a range of technological applications, including DNA sequencing, single molecule detection, and controlled drug delivery. In this spirit, numerous efforts have been made to develop polymer translocation-based sequencing devices, these efforts include findings and insights from theoretical modeling, simulations, and experimental studies. As much as the past and ongoing studies have added to the knowledge, the practical realization of low-cost, high-throughput sequencing devices, however, has still not been realized. There are challenges, the foremost of which is controlling the speed of translocation at the single monomer level, which remain to be addressed in order to use polymer translocation-based methods for sensing applications. In this article, we review the recent studies aimed at developing control over the dynamics of polymer translocation through nanopores.

Protein Condensation at Nanopore Entrances as Studied by Differential Scanning Calorimetry and Small-Angle Neutron Scattering

The condensation of globular myoglobin (Mb) at the pore entrances of mesoporous silica (MPS) with a series of pore diameters (4.2, 6.4, 7.7, and 9.0 nm) was examined by differential scanning calorimetry (DSC) and contrast-matching small-angle neutron scattering (CM-SANS) experiments. The DSC measurements were performed to estimate the amount of Mb adsorbed at two different adsorption sites, namely, the pore interior and the pore entrance regions. The CM-SANS measurements were conducted to observe condensation of Mb molecules at the pore entrance regions. Notably, the nanopore entrance with a diameter close to twice that of the Mb diameter was found to be the specific cavity to facilitate the condensation of globular Mb. The Mb condensation occurred at the entrances of the 6.4 nm pore during the adsorption uptake from concentrated Mb solutions, whereas the adsorption uptake from diluted Mb solutions induced the condensation of Mb at the entrances of the 7.7 nm pore.

Experimental study of a nanoscale translocation ratchet

Despite an extensive theoretical and numerical background, the translocation ratchet mechanism, which is fundamental for the transmembrane transport of biomolecules, has never been experimentally reproduced at the nanoscale. Only the Sec61 and bacterial type IV pilus pores were experimentally shown to exhibit a translocation ratchet mechanism. Here we designed a synthetic translocation ratchet and quantified its efficiency as a nanopump. We measured the translocation frequency of DNA molecules through nanoporous membranes and showed that polycations at the trans side accelerated the translocation in a ratchet-like fashion. We investigated the ratchet efficiency according to geometrical and kinetic parameters and observed the ratchet to be only dependent on the size of the DNA molecule with a power law [Formula: see text]. A threshold length of 3 kbp was observed, below which the ratchet did not operate. We interpreted this threshold in a DNA looping model, which quantitatively explained our results.

DsbA is a redox-switchable mechanical chaperone

DsbA is a ubiquitous bacterial oxidoreductase that associates with substrates during and after translocation, yet its involvement in protein folding and translocation remains an open question. Here we demonstrate a redox-controlled chaperone activity of DsbA, on both cysteine-containing and cysteine-free substrates, using magnetic tweezers-based single molecule force spectroscopy that enables independent measurements of oxidoreductase activity and chaperone behavior. Interestingly we found that this chaperone activity is tuned by the oxidation state of DsbA; oxidized DsbA is a strong promoter of folding, but the effect is weakened by the reduction of the catalytic CXXC motif. We further localize the chaperone binding site of DsbA using a seven-residue peptide which effectively blocks the chaperone activity. We found that the DsbA assisted folding of proteins in the periplasm generates enough mechanical work to decrease the ATP consumption needed for periplasmic translocation by up to 33%.

Effects of active crowder size and activity-crowding coupling on polymer translocation

Polymer translocation in complex environments is crucially important to many biological processes in life. In the present work, we adopted two-dimensional Langevin dynamics simulations to study the forced and unbiased polymer translocation dynamics in active and crowded media. The translocation time and probability are analyzed in terms of active force F_a, volume fraction φ and also the crowder size. The non-trivial active crowder size effect and activity-crowding coupling effect as well as the novel mechanism of unbiased translocation between two active environments with different active particle sizes are clarified. Firstly, for forced translocation, we reveal an intriguing non-monotonic dependence of the translocation time on the crowder size in the case of large activity. In particular, crowders of intermediate size similar to the polymer segment are proven to be the most favorable for translocation. Moreover, a facilitation-inhibition crossover of the translocation time with increasing volume fraction is observed, indicating a crucial activity-crowding coupling effect. Secondly, for unbiased translocation driven by different active crowder sizes, the translocation probability demonstrates a novel turnover phenomenon, implying the appearance of an opposite directional preference as the active force exceeds a critical value. The translocation time in both directions decreases monotonically with the active force. The asymmetric activity effect together with the entropic driving scenario provides a reasonable picture for the peculiar behavior observed in unbiased translocation.

Pore shapes effects on polymer translocation

We translocated polymers through pores of different shapes and interaction patterns in three dimensions by Langevin molecular dynamics. There were four simple cylindrical pores of the same length but with different diameters. The results showed that even though decreasing the pore diameter would always decrease the translocation velocity, it was strongly dependent on the shape of the increased pore diameter. Although increasing the pore diameter made the translocation faster in simple cylindrical pores, it was complicated in different pore shapes, e.g. increasing the diameter in the middle decreased the translocation velocity. Investigating polymer shapes through the translocation process and comparing the shapes by the cumulative waiting time for different pore structures reveals the non-equilibrium properties of translocation. Moreover, polymer shape parameters such as gyration radius, polymer center of mass, and average aspect ratio help us to distinguish different pore shapes and/or different polymers.

Stopped-Flow Dynamics Study on the Escape Behavior of Polyelectrolyte Macromolecules from Microgels: The Influence of the Path Length and Size

We reported the fabrication of several monodispersed poly(2-vinyl pyridine)-poly(N-isopropylacrylamide) (P2VP-PNIPAM) microgels including the P2VP core (non-cross-linked) and PNIPAM (cross-linked) shell by mature emulsion polymerization. The fast escape behavior (diffusion process) of linear P2VP chains through a porous PNIPAM layer was investigated by a pH jump stopped-flow apparatus. The time-dependent dynamic traces (corresponding to the scattered light intensity) decreased at the initial timescale of several seconds and then reached an apparent equilibrium, confirming the efficient escape of P2VP chains from microgels. Compared with the previously reported literature, such an accelerated escape process resulted from the sharply increased internal charge repulsive force caused by the protonation of P2VP moieties under acidic conditions. The obtained characteristic relaxation times by single exponential fitting of these kinetic traces were dependent on the final pH values, equilibrium temperatures, shell thickness (path length), and cross-linking density (mesh size). We believe that this work can provide an efficient way to investigate hindered diffusion, especially the initial rapid diffusion stage. Not only that, the proposed model can also provide theoretical guidance to some practical applications, such as membrane separation and the exocytosis phenomenon of intracellular proteins or macromolecular substances.

Crowding-Induced DNA Translocation through a Protein Nanopore

A crowded cellular environment is highly associated with many significant biological processes. However, the effect of molecular crowding on the translocation behavior of DNA through a pore has not been explored. Here, we use nanopore single-molecule analytical technique to quantify the thermodynamics and kinetics of DNA transport under heterogeneous cosolute PEGs. The results demonstrate that the frequency of the translocation event exhibits a nonmonotonic dependence on the crowding agent size, while both the event frequency and translocation time increase monotonically with increasing crowder concentration. In the presence of PEGs, the rate of DNA capture into the nanopore elevates 118.27-fold, and at the same time the translocation velocity decreases from 20 to 120 μs/base. Interestingly, the impact of PEG 4k on the DNA-nanopore interaction is the most notable, with up to ΔΔG = 16.27 kJ mol^-1 change in free energy and 764.50-fold increase in the binding constant at concentration of 40% (w/v). The molecular crowding effect will has broad applications in nanopore biosensing and nanopore DNA sequencing in which the strategy to capture analyte and to control the transport is urgently required.

Translocation through a narrow pore under a pulling force

We employ a three-dimensional molecular dynamics to simulate a driven polymer translocation through a nanopore by applying an external force, for four pore diameters and two external forces. To see the polymer and pore interaction effects on translocation time, we studied nine interaction energies. Moreover, to better understand the simulation results, we investigate polymer center of mass, shape factor and the monomer spatial distribution through the translocation process. Our results reveal that increasing the polymer-pore interaction energy is accompanied by an increase in the translocation time and decrease in the process rate. Furthermore, for pores with greater diameter, the translocation becomes faster. The shape analysis of the polymer indicates that the polymer shape is highly sensitive to the interaction energy. In great interactions, the monomers come close to the pore from both sides. As a result, the translocation becomes fast at first and slows down at last. Overall, it can be concluded that the external force does not play a major role in the shape and distribution of translocated monomers. However, the interaction energy between monomer and nanopore has a major effect especially on the distribution of translocated monomers on the trans side.

Trapped and non-trapped polymer translocations through a spherical pore

The polymer translocation through a spherical pore is studied using the Langevin dynamics simulation. The translocation events are classified into two types: one is the trapped translocation in which the entire polymer is trapped in the pore and the other is the non-trapped translocation where the pore cannot hold the whole polymer. We find that the trapped translocation is favored at large spheres and small external voltages. However, the monomer-pore attraction would lead to the non-monotonic behavior of the trapped translocation possibility out of all translocation events. Moreover, both the trapped and non-trapped translocation times are dependent on the polymer length, pore size, external voltage, and the monomer-pore attraction. There exist two pathways for the polymer in the trapped translocation: an actively trapped pathway for the polymer trapped in the pore before the head monomer arrives at the pore exit, and a passively trapped pathway for the polymer trapped in the pore while the head monomer is struggling to move out of the pore. The studies of trapped pathways can provide a deep understanding of the polymer translocation behavior.

Simulation study on the translocation of polyelectrolyte through conical nanopores

Experiments have suggested that the conical nanopore may be a reasonable sensor for the biopolymer analysis as it can provide high-resolution current signal. In this paper, we use Langevin dynamics simulation to study the translocation of charged polymer (polyelectrolyte) through three different conical nanopores, a single-conical nanopore with large entry and small exit (pore I), a single-conical nanopore with small entry and large exit (pore II), and a double-conical nanopore with the tip (narrowest place) at the middle (pore III). Simulation shows that the detailed translocation behaviors are of pore structure dependence. Pore I might be the most reasonable one for the polyelectrolyte analysis, especially at strong monomer-pore attraction, since it can efficiently reduce the polyelectrolyte speed at the tip. The simulation results are interpreted by the free energy profiles of the polyelectrolyte translocation through different pores and the time of individual monomer passing through the tips.

Theoretical study on the polymer translocation into an attractive sphere

We report a non-sampling model, combining the blob method with the standard lattice-based approximation, to calculate the free energy for the polymer translocation into an attractive sphere (i.e., spherical confined trans side) through a small pore. The translocation time is then calculated by the Fokker-Planck equation based on the free energy profile. There is a competition between the confinement effect of the sphere and the polymer-sphere attraction. The translocation time is increased due to the confinement effect of the sphere, whereas it is reduced by the polymer-sphere attraction. The two effects offset each other at a special polymer-sphere attraction which is dependent on the sphere size, the polymer length, and the driving force. Moreover, the entire translocation process can be divided into an uncrowded stage where the polymer does not experience the confinement effect of the sphere and a crowded stage where the polymer is confined by the sphere. At the critical sphere radius, the durations of the two (uncrowded and crowded) stages are the same. The critical sphere radius R^* has a scaling relation with the polymer length N as R^* ∼ N^β. The calculation results show that the current model can effectively treat the translocation of a three-dimensional self-avoiding polymer into the spherical confined trans side.

Bacterial Translocation Ratchets: Shared Physical Principles with Different Molecular Implementations: How bacterial secretion systems bias Brownian motion for efficient translocation of macromolecules

Secretion systems enable bacteria to import and secrete large macromolecules including DNA and proteins. While most components of these systems have been identified, the molecular mechanisms of macromolecular transport remain poorly understood. Recent findings suggest that various bacterial secretion systems make use of the translocation ratchet mechanism for transporting polymers across the cell envelope. Translocation ratchets are powered by chemical potential differences generated by concentration gradients of ions or molecules that are specific to the respective secretion systems. Bacteria employ these potential differences for biasing Brownian motion of the macromolecules within the conduits of the secretion systems. Candidates for this mechanism include DNA import by the type II secretion/type IV pilus system, DNA export by the type IV secretion system, and protein export by the type I secretion system. Here, we propose that these three secretion systems employ different molecular implementations of the translocation ratchet mechanism.

Temperature dependence of the translocation time of polymer through repulsive nanopores

The forced translocation of a polymer chain through repulsive nanopores was studied by using Langevin dynamics simulations. The polymer is in the compact globule state at low temperature and in the random coil state at high temperature. Simulation results show that the mean translocation time 〈τ〉 is highly dependent on the temperature T and the minimal 〈τ〉 is located near the coil-globule transition temperature. Moreover, the scaling behaviors 〈τ〉 ∼ N^α and 〈τ〉 ∼ F^-δ are studied, with N the polymer length and F the driving force inside the nanopore. Universal values α = 1.4 and δ = 0.85 are observed for the polymer in the random coil state. While for the polymer in the compact globule state, α decreases from α = 2 at weak driving to 1.2 at strong driving for short N and δ increases with decreasing T in the low F region, but we find universal exponents α = 1.6 for long N and δ = 0.85 in the large F region. Results show that polymer's conformation plays a much more important role than the diffusion coefficient in controlling the translocation time of the polymer chain.

Chaperone-driven polymer translocation through nanopore: Spatial distribution and binding energy

Chaperones are binding proteins working as a driving force in biopolymer translocation. They bind to the biopolymer near the pore and prevent its backsliding. Chaperones may have different spatial distributions. Recently, we showed the importance of their spatial distribution in translocation and its effects on the sequence dependency of the translocation time. Here we focus on homopolymers and exponential distribution. Because of the exponential distribution of chaperones, the energy dependency of the translocation time will change. Here we find a minimum in translocation time versus binding effective energy (EBE) curve. The same trend can be seen in the scaling exponent of time versus polymer length, [Formula: see text] ([Formula: see text]), when plotted against EBE. Interestingly in some special cases, e.g. chaperones of size [Formula: see text] and with an exponential distribution rate of [Formula: see text], the minimum even reaches to an amount of less than 1 ([Formula: see text]). We explain the possibility of this rare result. Moreover, based on a theoretical discussion we show that, by taking into account the velocity dependency of the translocation on polymer length, one can truly predict the value of this minimum.

Kinetics of DNA uptake during transformation provide evidence for a translocation ratchet mechanism

Horizontal gene transfer can speed up adaptive evolution and support chromosomal DNA repair. A particularly widespread mechanism of gene transfer is transformation. The initial step to transformation, namely the uptake of DNA from the environment, is supported by the type IV pilus system in most species. However, the molecular mechanism of DNA uptake remains elusive. Here, we used single-molecule techniques for characterizing the force-dependent velocity of DNA uptake by Neisseria gonorrhoeae We found that the DNA uptake velocity depends on the concentration of the periplasmic DNA-binding protein ComE, indicating that ComE is directly involved in the uptake process. The velocity-force relation of DNA uptake is in very good agreement with a translocation ratchet model where binding of chaperones in the periplasm biases DNA diffusion through a membrane pore in the direction of uptake. The model yields a speed of DNA uptake of 900 bp⋅s^-1 and a reversal force of 17 pN. Moreover, by comparing the velocity-force relation of DNA uptake and type IV pilus retraction, we can exclude pilus retraction as a mechanism for DNA uptake. In conclusion, our data strongly support the model of a translocation ratchet with ComE acting as a ratcheting chaperone.

Flow-induced translocation of star polymers through a nanopore

We study the flow-induced translocation of the star polymers through a nanopore using a hybrid simulation method that incorporates a lattice-Boltzmann approach for the fluid into a molecular dynamics model for the polymer. Our simulation demonstrates the existence of an optimal forward arm number of the star polymers captured by the nanopore, and illustrates its significance in determining the critical velocity flux of the star polymer translocation through the nanopore. Importantly, we find that the critical velocity flux of the star polymers is independent of the arm polymerization degree, but exhibits a linear dependence on the arm number. Based on previous scaling arguments and our simulation results, we conclude a linear dependence of the critical velocity flux on the arm number of the star polymers, which can successfully describe the dynamics of the star polymer translocation. Our simulation results rationalize the experimental results for the dependence of the critical velocity flux on the arm polymerization degree and the arm number of the star polymers, which provide new insights for the characterization and the purification of the star polymers.

Chaperone-assisted translocation of flexible polymers in three dimensions

Polymer translocation through a nanometer-scale pore assisted by chaperones binding to the polymer is a process encountered in vivo for proteins. Studying the relevant models by computer simulations is computationally demanding. Accordingly, previous studies are either for stiff polymers in three dimensions or flexible polymers in two dimensions. Here, we study chaperone-assisted translocation of flexible polymers in three dimensions using Langevin dynamics. We show that differences in binding mechanisms, more specifically, whether a chaperone can bind to a single site or multiple sites on the polymer, lead to substantial differences in translocation dynamics in three dimensions. We show that the single-binding mode leads to dynamics that is very much like that in the constant-force driven translocation and accordingly mainly determined by tension propagation on the cis side. We obtain β≈1.26 for the exponent for the scaling of the translocation time with polymer length. This fairly low value can be explained by the additional friction due to binding particles. The multiple-site binding leads to translocation the dynamics of which is mainly determined by the trans side. For this process we obtain β≈1.36. This value can be explained by our derivation of β=4/3 for constant-bias translocation, where translocated polymer segments form a globule on the trans side. Our results pave the way for understanding and utilizing chaperone-assisted translocation where variations in microscopic details lead to rich variations in the emerging dynamics.

Surface-adsorption-induced polymer translocation through a nanopore: Effects of the adsorption strength and the surface corrugation

The surface corrugation plays an important role in single polymer diffusion on attractive surfaces. However, its effect on dynamics of surface adsorption-induced polymer translocation through a nanopore is not clear. Using three-dimensional Langevin dynamics simulations, we investigate the dynamics of a flexible polymer chain translocation through a nanopore induced by the selective adsorption of translocated segments onto the trans side of the membrane. The translocation probability Ptrans increases monotonically, while the mean translocation time τ has a minimum as a function of the adsorption strength ɛ, which are explained from the perspective of the effective driving force for the translocation. With the surface being smoother, τ as well as the scaling exponent α of τ with the chain length N decreases. Finally, we show that the distributions of the translocation time are non-Gaussian even for strong adsorption at a moderate surface corrugation. A nearly Gaussian distribution of the translocation time is observed only for the smoothest surface we studied.

Translocation of a semiflexible polymer through a nanopore in the presence of attractive binding particles

We study the translocation dynamics of a semiflexible polymer through a nanopore from the cis into the trans compartment containing attractive binding particles (BPs) using the Langevin dynamics simulation in two dimensions. The binding particles accelerate the threading process in two ways: (i) reducing the back-sliding of the translocated monomer, and (ii) providing the pulling force toward the translocation direction. We observe that for certain binding strength (ε_{c}) and concentration (ρ) of the BPs, the translocation is faster than the ideal ratcheting condition as elucidated by Simon, Peskin, and Oster [M. Simon, C. S. Peskin, and G. F. Oster, Proc. Natl. Acad. Sci. USA 89, 3770 (1992)PNASA60027-842410.1073/pnas.89.9.3770]. The asymmetry produced by the BPs at the trans-side leads to similarities of this process to that of a driven translocation with an applied force inside the pore manifested in various physical quantities. Furthermore, we provide an analytic expression for the force experienced by the translocating chain as well as for the scaled mean first passage time (MFPT), for which we observe that for various combinations of N, ε, and ρ the scaled MFPT (〈τ〉/N^{1.5}ρ^{0.8}) collapses onto the same master plot. Based on the analysis of our simulation data, we provide plausible arguments with regard to how the scaling theory of driven translocation can be generalized for such a directed diffusion process by replacing the externally applied force with an effective force.

Translocation of polymers into crowded media with dynamic attractive nanoparticles

The translocation of polymers through a small pore into crowded media with dynamic attractive nanoparticles is simulated. Results show that the nanoparticles at the trans side can affect the translocation by influencing the free-energy landscape and the diffusion of polymers. Thus the translocation time τ is dependent on the polymer-nanoparticle attraction strength ɛ and the mobility of nanoparticles V. We observe a power-law relation of τ with V, but the exponent is dependent on ɛ and nanoparticle concentration. In addition, we find that the effect of attractive dynamic nanoparticles on the dynamics of polymers is dependent on the time scale. At a short time scale, subnormal diffusion is observed at strong attraction and the diffusion is slowed down by the dynamic nanoparticles. However, the diffusion of polymers is normal at a long time scale and the diffusion constant increases with the increase in V.

Equilibrium and dynamical properties of polymer chains in random medium filled with randomly distributed nano-sized fillers

The effect of randomly distributed nano-sized fillers on the equilibrium and dynamical properties of linear polymers is studied by using off-lattice Monte Carlo simulation.

Polymer translocation: the first two decades and the recent diversification

Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.

Dynamics and limitations of spontaneous polyelectrolyte intrusion into a charged nanocavity

We systematically investigate the spontaneous packaging mechanism of a single polyelectrolyte chain into an oppositely charged nanocavity by Langevin molecular dynamics simulations of a generic coarse-grained model. Intrusion dynamics and packaging rate, as well as the self-assembly process inside turn out to depend sensitively on the stiffness of the polyelectrolyte, the surface charge density inside the capsid, and the radius of the cavity. Further analysis shows that, depending on the stiffness, thermal fluctuations and charge inversion can be important factors to overcome barriers that slow down the intrusion and packaging dynamics. These results help advance our understanding of the function of charges on the inner surface of viral capsids and the possibility to design capsids as synthetic nanocarriers.

Langevin dynamics simulation on the translocation of polymer through α-hemolysin pore

The forced translocation of a polymer through an α-hemolysin pore under an electrical field is studied using a Langevin dynamics simulation. The α-hemolysin pore is modelled as a connection of a spherical vestibule and a cylindrical β-barrel and polymer-pore attraction is taken into account. The results show that polymer-pore attraction can help the polymer enter the vestibule and the β-barrel as well; however, a strong attraction will slow down the translocation of the polymer through the β-barrel. The mean translocation time for the polymer to thread through the β-barrel increases linearly with the polymer length. By comparing our results with that of a simple pore without a vestibule, we find that the vestibule helps the polymer enter and thread through the β-barrel. Moreover, we find that it is easier for the polymer to thread through the β-barrel if the polymer is located closer to the surface of the vestibule. Some simulation results are explained qualitatively by theoretically analyzing the free-energy landscape of polymer translocation.

Polymer translocation through a nanopore driven by binding particles: influence of chain rigidity

We investigate the influence of chain rigidity on the dynamics of polymer translocation in the presence of binding particles (BPs) through a nanopore using two-dimensional Langevin dynamics simulations. With increasing chain rigidity κ, the mean translocation time 〈τ〉 increases monotonically due to an increase in the radius of gyration and a decrease in the center of mass velocity. Particularly for weak binding, we further find that 〈τ〉 shows a power-law behavior with the persistence length lp. Analysis indicates a scaling relation between the average velocity of the center of mass of a chain 〈vc.m.〉 and lp. As the chain becomes stiffer, the distribution of the translocation time τ approximates the Gaussian distribution and gets broader with the peak position being shifted towards longer translocation time. The corresponding translocation coordinate smax of the maximum waiting time gets smaller with increasing chain rigidity. Finally, under an extremely low BP concentration, 〈τ〉 shows a minimum for small κ, while it decreases monotonically for large κ with increasing binding energy. Our results suggest a nontrivial effect of the intrinsic property of chains on the dynamics of polymer translocation driven by BPs.

Conformation-dependent translocation of a star polymer through a nanochannel

The translocation process of star polymers through a nanochannel is investigated by dissipative particle dynamics simulations. The translocation process is strongly influenced by the star arm arrangement as the polymer enters the channel, and a scaling relation between the translocation time [Formula: see text] and the total number of beads N tot is obtained. Qualitative agreements are found with predictions of the nucleation and growth model for linear block co-polymer translocation. In the intermediate stage where the center of the star polymer is at the channel entrance, the translocation time is found to have power law-dependence on the number of arms outside the channel and very weakly dependent on the number of arms in the channel. Increasing the total number of star arms also increases the star translocation time.

Study on the polymer translocation induced blockade ionic current inside a nanopore by Langevin dynamics simulation

The blockade ionic current inside a nanopore due to polymer translocation is studied using a three-dimensional Langevin dynamics method. The blockade current IB is dependent on the polymer length N, polymer configuration, polymer-pore interaction, and charge of the polymer. The behavior of IB can be explained using four factors: (1) the volume vacancy fraction fV inside the pore; (2) the conformation of the polymer; (3) the location of the polymer inside the pore; and (4) the total charge Ztot inside the pore. We find that IB increases with fV but decreases with increasing |Ztot|. The influence of the polymer's conformation is complex, dependent on the size of polymer RG and the cross-sectional size of the pore s. A compact conformation can decrease IB when RG > s but increase IB when RG < s. For the latter case, the conformation of the polymer is too small to block the pore, thus providing a broad passage for the ions. At the same fV, monomers will locate close to the surface with a large polymer-pore attraction, which also provides a large IB.

Translocation of a polymer through a nanopore across a viscosity gradient

The translocation of a polymer through a pore in a membrane separating fluids of different viscosities is studied via several computational approaches. Starting with the polymer halfway, we find that as a viscosity difference across the pore is introduced, translocation will predominately occur towards one side of the membrane. These results suggest an intrinsic pumping mechanism for translocation across cell walls which could arise whenever the fluid across the membrane is inhomogeneous. Somewhat surprisingly, the sign of the preferred direction of translocation is found to be strongly dependent on the simulation algorithm: for Langevin dynamics (LD) simulations, a bias towards the low viscosity side is found while for Brownian dynamics (BD), a bias towards the high viscosity is found. Examining the translocation dynamics in detail across a wide range of viscosity gradients and developing a simple force model to estimate the magnitude of the bias, the LD results are demonstrated to be more physically realistic. The LD results are also compared to those generated from a simple, one-dimensional random walk model of translocation to investigate the role of the internal degrees of freedom of the polymer and the entropic barrier. To conclude, the scaling of the results across different polymer lengths demonstrates the saturation of the directional preference with polymer length and the nontrivial location of the maximum in the exponent corresponding to the scaling of the translocation time with polymer length.

Effects of an attractive wall on the translocation of polymer under driving

The effects of an attractive wall at the trans side on the translocation of an eight-site bond-fluctuation model (BFM) polymer through a pore in a membrane under driving are simulated by the dynamic Monte Carlo method. The attractive wall shows two contrary effects: its excluded volume effect reduces configuration entropy and thus hinders the translocation of the polymer, while its attraction decreases the energy and thus accelerates the translocation. At a critical polymer-wall interaction ε* ≈- 1, we find that the two effects compensate each other and the translocation time τ is roughly independent of the separation distance between the wall and the pore. The value ε* ≈- 1 is roughly equal to the critical adsorption point for the BFM polymer. Moreover, the value of the critical attraction is roughly independent of chain length N and chemical potential difference Δμ. At last, a scaling relation τ ∼ N(α) is observed for polymer translocation at a high value of NΔμ. Though the translocation time is highly dependent on the polymer-wall interaction and pore-wall separation distance, the exponent α is always about 1.30 ± 0.05 so long as NΔμ is large enough.